Compact inner product encryption from LWE

Abstract

Predicate encryption provides fine-grained access control and has attractive applications. In this paper, We construct an compact inner product encryption scheme from the standard Learning with Errors (LWE) assumption that has compact public-key and achieves weakly attribute-hiding in the standard model. In particular, our scheme only needs two public matrices to support inner product over vector space Zqlogλ, and (λ/ log λ) public matrices to support vector space Zqλ. Our construction is the first compact functional encryption scheme based on lattice that goes beyond the very recent optimizations of public parameters in identity-based encryption setting. The main technique in our compact IPE scheme is a novel combination of IPE scheme of Agrawal, Freeman and Vaikuntanathan (Asiacrypt 2011), fully homomorphic encryption of Gentry, Sahai and Waters (Crypto 2013) and vector encoding schemes of Apon, Fan and Liu (Eprint 2017).